Optimal Korn’s inequality for solenoidal vector fields on a periodic slab. (English) Zbl 1263.35012

Summary: We obtain the best constant in Korn’s inequality for solenoidal vector fields on a periodic slab which vanish on a part of its boundary. To do this we consider the Stokes equations with Dirichlet boundary conditions, following H. Ito [Math. Methods Appl. Sci. 17, No. 7, 525–549 (1994; Zbl 0801.73014); Japan J. Ind. Appl. Math. 16, No. 1, 101–121 (1999; doi:10.1007/BF03167526)].


35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
35B45 A priori estimates in context of PDEs


Zbl 0801.73014
Full Text: DOI Euclid


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